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Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems

Brandão, Fernando G. S. L. and Cramer, Marcus (2015) Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems. 18. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20160608-092309554

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Abstract

We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of N spins arranged on a d-dimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up to O(N^(1/(d+1))) spins. The proof rests on a variant of the Berry-Esseen theorem for quantum lattice systems and ideas from quantum information theory.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1502.03263arXivDiscussion Paper
ORCID:
AuthorORCID
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:FB acknowledges EPSRC for financial support. MC acknowledges the EU Integrated Project SIQS and the Alexander von Humboldt foundation for financial support. Part of this work was done while FB was visiting the Simons Institute for the Theory of Computing in the program Quantum Hamiltonian Complexity.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
European UnionUNSPECIFIED
Alexander von Humboldt FoundationUNSPECIFIED
Issue or Number:18
Record Number:CaltechAUTHORS:20160608-092309554
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160608-092309554
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67759
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Jun 2016 16:43
Last Modified:03 Oct 2019 10:08

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